--- - |2 Abstract Natural languages vary widely in the degree to which they make use of nested compositional structure in their grammars. It has long been noted by linguists that the languages historically spoken in small communities develop much deeper levels of compositional embedding than those spoken by larger groups. Recently, this observation has been confirmed by a robust statistical analysis of the World Atlas of Language Structures. In order to examine this connection mechanistically, we propose an agent‐based model that accounts for key cultural evolutionary features of language transfer and language change. We identify transitivity as a physical parameter of social networks critical for the evolution of compositional structure and the hierarchical patterning of scale‐free distributions as inhibitory. - Cognitive Science, EarlyView.